The spatial resolution of a source image or video frame is often larger than the screen size of a handheld device. Consequently, image downsizing or video transcoding with spatial resolution down-sampling is performed, typically at the server side of the service provider, to reduce the spatial resolution of the source image or video frame in order to fit the display screen of the end device. Image or video frame resizing is conventionally performed in the pixel, or spatial, domain through a low-pass filtering operation followed by a downsampling process. However, for JPEG images, and video frames formatted according to common standards, such as H.26x series standards and MPEG-x series standards, the image and video frames are already in a compressed format in the frequency domain and the resized JPEG images or video frames must be transmitted in their compressed format. Thus, spatial domain resizing of such compressed images or video frames requires that the images be fully decoded into the pixel domain, resized through low-pass filtering, downsampled, and recompressed. Though effective, this brute force approach is undesirable due to its high computational cost.
The computational complexity can be reduced by resizing the images in the frequency domain. Some of the suggested approaches use a filter matrix whose entries depend on the discrete cosine transform (DCT) basis functions. However, these approaches are only designed for resizing images by a power of 2 or a few specific ratios. In practical applications arbitrary resizing ratios are required since the spatial resolution, or the dimension of the source image, is arbitrary.
Arbitrary ratio resizing methods in the DCT domain have also been proposed. In one such method, an 8×8 downsized block is reconstructed from neighboring input blocks and corresponding shift matrices in the DCT domain. In another approach, the arbitrary ratio resizing is achieved by upsizing the image through zero padding, and then downsizing it through high-frequency DCT coefficient truncation. Both of these arbitrary ratio resizing methods in the DCT domain show good peak signal-to-noise ratio (PSNR) and lower computational complexity when compared with the spatial-domain resizing methods.
However, there are still two problems associated with these previously proposed arbitrary ratio resizing algorithms in the DCT domain. First, they are still computationally expensive. Second, both approaches are difficult to implement for practical applications. For most practical applications, such as web browsing or video game playing on handheld device, the spatial resolution of each source image varies even though the screen size of the device is fixed. Therefore, the resizing ratio is not only arbitrary, but varies from image to image as well. For each different resizing ratio, the first approach requires a large number of different matrices to be calculated and stored in advance. The second approach requires fast implementation of DCT and inverse discrete cosine transform (IDCT) operations at every possible length, which is nontrivial even though some fast implementations for composite lengths exist.
Therefore, it is desirable to provide a fast arbitrary ratio image resizing approach in the DCT domain that is not only easily implemented for practical applications, but also reduces the computational complexity as compared to previous approaches.